Let A be a positive bounded linear operator acting on a complex Hilbert space H, • | • . Let ω A (T ) and T A denote the A-numerical radius and the A-operator seminorm of an operator T acting on the semi-Hilbertian space H, • | • A respectively, where x | y A := Ax | y for all x, y ∈ H. In this paper, we show that 1 4